cp's OEIS Frontend

A170258 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170258 #8 Oct 23 2024 16:46:52
%S A170258 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A170258 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A170258 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A170258 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170258 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A170258 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170258 <a href="/index/Rec#order_41">Index entries for linear recurrences with constant coefficients</a>, signature (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).
%F A170258 G.f. (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170258 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170258 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170258 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170258 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170258 1)/(28*t^41 - 7*t^40 - 7*t^39 - 7*t^38 - 7*t^37 - 7*t^36 - 7*t^35 -
%F A170258 7*t^34 - 7*t^33 - 7*t^32 - 7*t^31 - 7*t^30 - 7*t^29 - 7*t^28 - 7*t^27 -
%F A170258 7*t^26 - 7*t^25 - 7*t^24 - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 -
%F A170258 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 -
%F A170258 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 -
%F A170258 7*t + 1)
%t A170258 coxG[{41,28,-7}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 23 2024 *)
%K A170258 nonn
%O A170258 0,2
%A A170258 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009